Fungal tip growth arising through a codimension-1 global bifurcation

T.G. De Jong, A.E. Sterk, H.W. Broer

OnderzoeksoutputAcademicpeer review

2 Citaten (Scopus)


Tip growth is a growth stage which occurs in fungal cells. During tip growth, the cell exhibits continuous extreme lengthwise growth while its shape remains qualitatively the same. A model for single celled fungal tip growth is given by the Ballistic Aging Thin viscous Sheet (BATS) model, which consists of a five-dimensional system of first-order differential equations. The solutions of the BATS model that correspond to fungal tip growth arise through a codimension-1 global bifurcation in a two-parameter family of solutions. In this paper we derive a toy model from the BATS model. The toy model is given by two-dimensional system of first-order differential equations which depend on a single parameter. The main achievement of this paper is a proof that the toy model exhibits an analogue of the codimension-1 global bifurcation in the BATS model. An important ingredient of the proof is a topological method which enables the identification of the bifurcation points. Finally, we discuss how the proof may be generalized to the BATS model.

Originele taal-2English
Aantal pagina's20
TijdschriftInternational Journal of Bifurcation and Chaos
Nummer van het tijdschrift7
StatusPublished - 2020

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